Question

A very long insulating cylindrical shell of radius 6.00 cm carries a charge of 8.50 μC/m (linear charge density) spreading uniformly over its outer surface. What would a voltmeter read if it is connected between (a) the surface of the cylinder and 4.00 cm away (outward) from the surface, and (b) the surface and a point 1.00 cm from the central axis of the cylinder?

Answer 1

(a). The potential is 78.0 kV.

(b). The potential is zero.

Step-by-step explanation:

Given that,

Radius = 6.00

Charge density = 8.50 μC/m

(a). The surface of the cylinder and 4.00 cm away from the surface,

We need to calculate the voltage

Using formula of potential

`V=(\lambda)/(2\pi\epsilon_(0))ln((r)/(R))`

Put the value into the formula

`V=(8.5*10^(-6))/(2\pi*8.85*10^(-12))ln((6+4)/(6))`

`V=78.0\ kV`

(b). The surface and a point 1.00 cm from the central axis of the cylinder

Here, r = R

We need to calculate the voltage

Using formula of potential

`V=(\lambda)/(2\pi\epsilon_(0))ln((r)/(R))`

Put the value into the formula

`V=(8.5*10^(-6))/(2\pi*8.85*10^(-12))ln(1)`

`V=0\ kV`

Hence, (a). The potential is 78.0 kV.

(b). The potential is zero.